Use of logit transformation within statistical analyses of experimental results obtained as proportions: example of method validation experiments and EQA in flow cytometry

Abstract

In laboratory medicine, measurement results are often expressed as proportions of concentrations or counts. These proportions have distinct mathematical properties that can lead to unexpected results when conventional parametric statistical methods are naively applied without due consideration in the analysis of method validation experiments, quality assessments, or clinical studies. In particular, data points near 0% or 100% can lead to misleading analytical conclusions. To avoid these problems, the logit transformation—defined as the natural logarithm of the proportion/(1-proportion)—is used. This transformation produces symmetric distributions centered at zero that extend infinitely in both directions without upper or lower bounds. As a result, parametric statistical methods can be used without introducing bias. Furthermore, homogeneity of variances (HoV) is given. The benefits of this technique are illustrated by two applications: (i) flow cytometry measurement results expressed as proportions and (ii) probabilities derived from multivariable models. In the first case, naive analyses within external quality assessment (EQA) evaluations that lead to inconsistent results are effectively corrected. Second, the transformation eliminates bias and variance heterogeneity, allowing for more effective precision estimation. In summary, the logit transformation ensures unbiased results in statistical analyses. Given the resulting homogeneity of variances, common parametric statistical methods can be implemented, potentially increasing the efficiency of the analysis.